What is the integral from-1 to 2 of (x-1)(2x+3) ?

The integral from-1 to 2 of (x-1)(2x+3) is -3/2

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integral from-1 to 2 of (x-1)(2x+3)

\int_{- 1}^{2} (x - 1) (2 x + 3) d x

- \frac{3}{2}

Decimal

- 1.5

Solution steps

\int_{- 1}^{2} (x - 1) (2 x + 3) d x

Expand

(x - 1) (2 x + 3) : 2 x^{2} + x - 3

= \int_{- 1}^{2} 2 x^{2} + x - 3 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{- 1}^{2} 2 x^{2} d x + \int_{- 1}^{2} x d x - \int_{- 1}^{2} 3 d x

\int_{- 1}^{2} 2 x^{2} d x = 6

\int_{- 1}^{2} x d x = \frac{3}{2}

\int_{- 1}^{2} 3 d x = 9

= 6 + \frac{3}{2} - 9

Simplify

6 + \frac{3}{2} - 9 : - \frac{3}{2}

= - \frac{3}{2}

What is the integral from-1 to 2 of (x-1)(2x+3) ?
The integral from-1 to 2 of (x-1)(2x+3) is -3/2